Finite Group Databasebeta

← #37532717

Subgroups — #37532717

Order 23168.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041878C211yesmaximal, characteristic
2#26041592C211yesmaximal, characteristic
3#26041210C211yesmaximal, characteristic, complemented
4#26041016C211yesmaximal, characteristic, complemented
5#26041014C211yesmaximal, characteristic
6#26041004C211yesmaximal, characteristic, complemented
7#483×C181C211yesmaximal, characteristic, complemented
8#19153811—21no—
9#19153807—21no—
10#19153801—21no—
11#19153800—21no—
12#19153792—21no—
13#19153790C2211yescharacteristic
14#19153776—21no—
15C2×#15668428—21no—
16C2×#15668428C2211yescharacteristic
17#19153749—21no—
18#19153736—21no—
19C22⋊#13089678C2211yescharacteristic
20#19153723—21no—
21#19153723C2211yescharacteristic
22C22⋊Q8×C181C2211yescharacteristic
23C2×C4⋊C4×C181C2211yescharacteristic
24#106×C181—21no—
25#103×C181—21no—
26C22⋊C8×C181C2211yescharacteristic
27C2×D724D411yescharacteristic
28C2×C22⋊D181—21no—
29C22×Dic181—21no—
30C22×Dic181D411yescharacteristic
31C22×Dic181D411yescharacteristic
32C2×C4×D181—21no—
33C2×#13089678—21no—
34C4⋊Dic181—21no—
35C4⋊Dic181—21no—
36C4⋊Dic181D411yescharacteristic
37#15668428—21no—
38#15668428—21no—
39#15668428—21no—
40#15668428—42no—
41#15668426—21no—
42#15668426—21no—
43#15668426—21no—
44#15668426—21no—
45C4×Dic181—21no—
46C2×Q8×C181D411yescharacteristic
47C22×C4×C181—21no—
48C22×C4×C181C2311yescharacteristic
49C2×C8×C181—21no—
50C4⋊C4×C181—21no—
51C4⋊C4×C181—21no—
52C4⋊C4×C181—21no—
53C4⋊C4×C181D411yescharacteristic
54C22⋊C4×C181—21no—
55C22×D181—21no—
56D724—41no—
57C22⋊D181—41no—
58C22⋊D181—41no—
59C2×Dic181—22no—
60C2×Dic181—21no—
61C2×Dic181—21no—
62C2×Dic181—21no—
63C2×Dic181—21no—
64C2×Dic181—21no—
65C2×Dic181—41no—
66C2×Dic181—41no—
67C2×Dic181—41no—
68C4×D181—81no—
69#13089678—41no—
70C23×C181C2×D411yescharacteristic
71Q8×C181—41no—
72C2×C4×C181—21no—
73C2×C4×C181—21no—
74C2×C4×C181—41no—
75C2×C4×C181—41no—
76C2×C4×C181—41no—
77C2×C4×C181—41no—
78C2×C4×C181C2×D411yescharacteristic
79C2×C4×C181C2×D411yescharacteristic
80C8×C181—41no—
81C22×C181—21no—
82C22×C181—21no—
83C22×C181#12011yescharacteristic
84C22×C181#13511yescharacteristic
85C22×C181AGL(1,ℤ/8)11yescharacteristic
86C2×D181—41no—
87C2×D181—41no—
88C2×D181—41no—
89C4×C181—21no—
90C4×C181—21no—
91C4×C181—41no—
92C4×C181—41no—
93C4×C181—81no—
94Dic181—42no—
95Dic181—41no—
96Dic181—41no—
97Dic181—41no—
98C2×C181—21no—
99C2×C181—21no—
100C2×C181#44911yescharacteristic
101C2×C181#45611yescharacteristic
102C2×C181#45811yescharacteristic
103D181—81no—
104C181#160911yescharacteristic, complemented, Sylow
105#1609—1811nomaximal, Sylow
106#539—1811no—
107#483D18111yescharacteristic, complemented
108#480—1811no—
109#398—1811no—
110#328—1811no—
111#327—1811no—
112#324—1811no—
113#126—3621no—
114#125—3621no—
115#123—3621no—
116#123—3621no—
117C22⋊Q8—3621no—
118C22⋊Q8C2×D18111yescharacteristic
119#121—1811no—
120C4×D4—3621no—
121C2×C4⋊C4—3621no—
122C2×C4⋊C4—1811no—
123C2×C4⋊C4C2×D18111yescharacteristic
124#107—3621no—
125#106—21no—
126#103—21no—
127#102—3621no—
128C22⋊C8—1811no—
129C22⋊C8C2×D18111yescharacteristic
130#95—3621no—
131#95—1811no—
132C2×Q8C22⋊D18111yescharacteristic
133C2×D4—3621no—
134C2×D4—1811no—
135C22×C4—21no—
136C22×C4—3621no—
137C22×C4—3621no—
138C22×C4—1811no—
139C22×C4—1811no—
140C22×C4C22×D18111yescharacteristic
141C2×C8—21no—
142C2×C8—3621no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—3621no—
147C4⋊C4—3621no—
148C4⋊C4—3621no—
149C4⋊C4—3621no—
150C4⋊C4—3621no—
151C4⋊C4—1811no—
152C4⋊C4—7242no—
153C4⋊C4C22⋊D18111yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—3621no—
156C22⋊C4—3621no—
157C22⋊C4—3621no—
158C22⋊C4—3621no—
159C42—3621no—
160C23—3621no—
161C23D4×D18111yescharacteristic
162Q8—41no—
163D4—7241no—
164D4—7241no—
165D4—7241no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—3622no—
173C2×C4—3621no—
174C2×C4—3621no—
175C2×C4—3621no—
176C2×C4—3621no—
177C2×C4—3621no—
178C2×C4—14481no—
179C2×C4—7241no—
180C2×C4—7241no—
181C2×C4—7241no—
182C2×C4D4×D18111yescharacteristic
183C2×C4C2×C22⋊D18111yescharacteristic
184C8—41no—
185C8—7241no—
186C22—21no—
187C22—21no—
188C22—7241no—
189C22—7241no—
190C22—7241no—
191C22#1915378411yescharacteristic
192C22#1915383711yescharacteristic
193C22#1915384311yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—81no—
199C4—7242no—
200C4—7241no—
201C4—7241no—
202C4—7241no—
203C2—21no—
204C2—21no—
205C2—14481no—
206C2#2604142311yescharacteristic
207C2#2604146011yescharacteristic
208C2#2604146811yescharacteristic
subgroupG/H
centerC22#19153784
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#483×C181C2
socleC22×C181#120
prime radical#19153790C22
hypercenter#483D181
hypocenterC181#1609
LCSG ▷ C22×C4×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #26041210C2semidirect
4. #26041016C2semidirect
6. #26041004C2semidirect
7. #483×C181C2semidirect
104. C181#1609semidirect
107. #483D181semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260418782
#260415922
#260412102
#260410162
#260410142
#260410042
#483×C1812
#1609181